Atkin-Lehner |
3- 11- 19- 37- |
Signs for the Atkin-Lehner involutions |
Class |
69597k |
Isogeny class |
Conductor |
69597 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
975360 |
Modular degree for the optimal curve |
Δ |
120169785950973 = 316 · 11 · 193 · 37 |
Discriminant |
Eigenvalues |
2 3- 4 -4 11- 0 5 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-170193,-27019539] |
[a1,a2,a3,a4,a6] |
Generators |
[149730:20479141:8] |
Generators of the group modulo torsion |
j |
747861652545089536/164841956037 |
j-invariant |
L |
15.846604592207 |
L(r)(E,1)/r! |
Ω |
0.23505520667725 |
Real period |
R |
11.236087056088 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000588 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23199f1 |
Quadratic twists by: -3 |